Exactly positioning and aligning objects
Here are some useful tips for precise modeling in Blender:

01) Set your units to milimeters
Properties Panel->Scene->Units->Length  



02) Set snapping to Increments
and enable Absolute snapping.  



03) Use orthographic view and side views
This allows you to use grid better, and align precisely
Orthographic view shortcut: Numpad 5
Viewpoint shortcut: ~ or use Numpad numbers.

Switch to orthographic view and out


Use ~ to switch views


04) Make use of Quad View


05) Learn to use 3D cursor and work with Object origin.
These are very powerful together for precise object alignment.


06) Adjust your grid scale.
The default setting is good for most situations, but sometimes you may need to adjust it.



07) Blender is no CAD, but it will get you there :).
And as @Leander said - tinyCAD addon.
Enable it in Preferences->Addons  (and Save preferences)